MIDAS Civil Curved Bridge Analysis Comparison of Methods & Construction Staging Tom Less, PE, SE, ENV SP Team Leader, Bridge/Structural Engineer
Introduction – Curved Bridge Modeling Types of Models to be Discussed • Traditional Girder Line with V-Load Analysis • Two- Dimensional (Grillage) Analysis and “Grillage 2D+” • Three-Dimensional Analysis Project Background – CVG CONRAC Unit 2 • Comparison of Model Creation and Loading • Comparison of Results from Modeling Approaches Construction Sequencing and Constructability • Purpose • Implementation within Programs • Comparison – Grillage and All-plate Project – ODOT GUE-513-08.65, Temporary Supports and Staged Construction Conclusions
Modeling – Girder Line & V-Load Girder Line Modeling • Uses standard AASHTO LLDF • Can be done in minimal time, not a complicated analysis • In this case used Merlin DASH • Use results to populate a V-Load analysis spreadsheet or hand calculation, and iterate with a target utilization ratio (1.00 – anticipated V-Load increase) • Typically produces good results for dead load approximations for noncomposite and composite bridges with radial crossframes or bracing • Live load can be much more variable based on lateral stiffness, geometry, and resulting intermittent influence surface • Typically a good method for preliminary engineering purposes
Modeling – Girder Line & V-Load V-Load Theory • Many references available • Essentially, straighten girder and analyze based on true length as a straight member, then apply external forces to induce resultant internal forces corresponding to the curved structure under vertical loads • From past projects, results have been very close to MIDAS Civil or other FEM for larger radii, say R > 1000-ft • Per AASHTO Section C4.6.2.2.4 has a number of limitations which do not qualify for required analysis methods for curved structures and may underestimate deflections, reactions, twist Figure from Horizontally Curved I-Girder Bridge Analysis: V-Load Method By Grubb, M.A.
Modeling – Two-Dimensional (Grillage) Grillage Analysis • Uses beam elements for each beam/girder and a grid, usually plates attached to the same nodes as beam elements, but with different offset (eccentric beam) • Alternatively, primary beam elements are used with full composite section properties, and secondary virtual beams are used for load distribution • Provides a more accurate distribution of live loads through influence surface • Lateral stiffness of deck is not modeled using this approach • Superimposed dead loads are distributed more accurately, however internal forces due to curvature are not captured
Modeling – Two-Dimensional+ (Grillage) 2D+ Grillage Analysis/Limited 3D Analysis • Similar to standard grillage, but with multiple sets of nodes with rigid links (master-slave) • Beams/girders are modeled using beam elements then rigid linked nodes modeling the deck plates and nodes for crossframe members in 3D • Provides an accurate distribution of live loads through influence surface • Lateral stiffness of crossframes and deck are modeled using this approach • Internal forces are captured using this approach, appropriate for curved girder design • In MIDAS, this is the default for the “Deck as Plate, Beam as Frame” modeling approach • The “All Frame” modeling approach also uses this method, but with the deck modeled by virtual transverse beams • Seventh degree of freedom included for warping effects
Modeling – Two-Dimensional+ (Grillage) 2D+ Grillage Analysis/Limited 3D Analysis Tip: Renumber nodes & elements by beam/girder to 10001-10xxx (Girder 1) 20001-20xxx (Girder 2) Makes manipulation and output much easier/quicker
Modeling – Three-Dimensional Full 3D Analysis • Similar to the Grillage+, but the beam is split into plate elements for each flange and web, in addition to plates for the deck • Provides an accurate distribution of live loads through influence surface • Lateral stiffness of crossframes and deck are modeled using this approach • Internal forces are captured using this approach, appropriate for curved girder design • Effects of tension-field action can be captured for shear • Girder/Beam rotations can be explicitly extracted – very important for construction cases in highly curved members • In MIDAS, this is the “All Plate” modeling approach
Modeling – Three-Dimensional Full 3D Analysis • Effects of tension-field action, post-buckling web strength
Modeling – Three-Dimensional Full 3D Analysis
Modeling Types Where to find in MIDAS:
Project Background – CVG CONRAC CVG Airport (Cincinatti)
Project Background – CVG CONRAC
Project Background – CVG CONRAC Original Condition Final Proposed Condition
Project Background – CVG CONRAC MSE Buildup Three Elevated Structures • Unit 1: Straight Rolled Beams • Unit 2: Curved Plate Girders • Unit 3: Prestressed I Beams
Project Background – CVG CONRAC Unit 2: Curved Steel Plate Girder Bridge • R = 200.00 ft • Minimum Girder R = 181.25 ft • Dc = 28 ⁰ 38’ 52” • Δ = 135.73⁰ • All crossframes and girders radial • 8 Spans, range from 48.5-ft to 68-ft
Project Background – CVG CONRAC Site and Geometric Constraints • Access below, multiple entry/exits • Plate mill runs, need to make sure it is possible to cut
Project Background – CVG CONRAC Shop splice versus field splice considerations • From AISC, there are guidelines to determine if cost effective • Analyzed to determine for this bridge, would require 0.5” - 0.625” thickness differential in field section from positive moment to negative moment. • Example: 16” x 80 lbs/in = 1280 lbs
Unit 2 Modeling – Preliminary Engineering • V-Load Analysis used during preliminary engineering • Predicted max ~11% increase in moments due to curvature • Designed for 0.85 Utility Ratio to account for girder warping and secondary effects • Estimated 5.5 kips for cross frame forces due to curvature effects
Unit 2 Modeling – Preliminary Engineering • V-Load Analysis used during preliminary engineering • Note that grillage and plate model results showed significantly higher crossframe forces than the V-load • Sizes: Preliminary (V-Load) Final (Grillage/All-Plate)
Unit 2 Modeling – Detailed Design, Grillage+ • A Grillage+ model in MIDAS with beams as frame was used for the detailed design • Tips: • Node and Beam Element Numbering is key • Checked the geometry created by wizard through CAD by using a scratch basemap with origin and angle aligned to MIDAS output • Note that some variation occurs through composite girder wizard due to conversion to metric and concatenation occurring during the wizard generation • Local Coordinates – use geometry and excel to develop the local angle (Beta Angle) at each node then paste into MIDAS menu, β i = 90 + tan -1 ( Δ y i / Δ x i ); where Δ y i and Δ x i are distances from the MIDAS center point/origin to the nodal location (x i , y i ). • Similar geometry and excel can be used to calculate “length along” the beam at each node for output to plans • Bearing conditions and boundary conditions are a critical consideration • By default MIDAS is performing a No Load Fit (NLF) analysis. This is a very important distinction and should be indicated on the plans for the fabricator.
Unit 2 Modeling – Detailed Design, Grillage+ I recommend the presentation by AISC, “Top 10 Changes in the 8 th Edition AASHTO LRFD Steel Specifications” if you have not watched it. The handouts are available here: https://www.aisc.org/webinarhandouts121317/
Additional Camber Consideration • When determining camber, if Radii is greater than 1000-ft need to account for additional camber from settling of the curved structure per AASHTO 6.7.7.3
Unit 2 Modeling – Comparisons • MIDAS Grillage+ versus LEAP Steel Grillage Feature MIDAS LEAP Steel Tabular Input X • LEAP uses a STAAD.Pro Engine for analysis Model Readily Accessible X • LEAP Steel serves as a GUI & Wizard Tabular Output X X Output Sorting Functions X • STAAD Model is accessible, but is deep in directory Detailed Calculations Output X X Data Restricting Functions X • LEAP model is faster to assemble and run Visual Output X Visual Display of Live Loads for Max Effect X • LEAP output is more difficult to use (at least currently) • Limited data sorting and exclusion • Limited capacity for visual representation of data, compared with MIDAS • The above is my personal opinion (disclaimer)
Unit 2 Modeling – Comparisons
Unit 2 Modeling – Comparisons • MIDAS Grillage+ versus MIDAS All Plate
Unit 2 Modeling – Comparisons • MIDAS Grillage versus LEAP Grillage Moment/Flange Stresses
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